Question 1

Which of the following best describes the physical meaning of capacitance for a parallel-plate capacitor?

Accepted Answer

The amount of charge stored per unit potential difference between the plates.

Question 2

A parallel-plate capacitor has plates of area $$A$$ separated by a distance $$d. $$What is the correct formula for its capacitance in vacuum?

Accepted Answer

$$C = \$$varepsilon_0$$ \dfrac{A}{d}$$

Question 3

If the charge on a parallel-plate capacitor is doubled while the plate separation and area remain constant, what happens to the potential difference across the plates?

Accepted Answer

It doubles.

Question 4

Which of the following correctly expresses the energy stored in a capacitor in terms of its capacitance $$C$$ and the potential difference $$V$$ across it?

Accepted Answer

$$U = \dfrac{1}{2} C V^2$

Question 5

A cylindrical capacitor consists of two coaxial cylinders of length $$L$$, inner radius $$r_a$$, and outer radius $$r_b. $$What is the correct formula for its capacitance?

Accepted Answer

$$C = 2 \pi \$$varepsilon_0$$ \dfrac{L}{\ln(r_b/r_a)}$$

Question 6

Two capacitors, $$C_1 = 47$ pF and C_2$ = 15 pF$$, are connected in series. What is their equivalent capacitance?

Accepted Answer

$$C_{eq} = 11.4 pF$$

Question 7

Which of the following statements is true for capacitors connected in parallel?

Accepted Answer

They all have the same potential difference across them.

Question 8

A dielectric material with dielectric constant $$K is $$inserted between the plates of a capacitor while the charge is kept constant. What happens to the electric field between the plates?

Accepted Answer

It decreases by a factor of $$K.$$

Question 9

Which of the following best describes the behavior of polar molecules in a dielectric when an external electric field is applied?

Accepted Answer

They align with the field, creating an induced surface charge.

Question 10

A parallel-plate capacitor with area $$A = 0.2 m$^2$$ and separation $$d = 1 cm is $$connected to a $$3 kV $$battery. What is the free surface charge density $$\sigma_{free} on $$the plates? ($$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$ F/m)

Accepted Answer

$$\sigma_{free} = \$$varepsilon_0$$ \dfrac{V}{d}$$

Question 11

What is the energy density $$u$$ stored in the electric field of a parallel-plate capacitor?

Accepted Answer

$$u = \dfrac{1}{2} \$$varepsilon_0$$ E^2$

Question 12

A spherical capacitor consists of two concentric spheres of radii $$r_a$$ and $$r_b$$ ($$r_b \u003e r_a). $$What is the correct formula for its capacitance?

Accepted Answer

$$C = 4 \pi \$$varepsilon_0$$ \dfrac{r_a r_b}{r_b - r_a}$$

Question 13

If a dielectric with dielectric constant $$K is $$inserted into a capacitor connected to a battery (constant $$V$$), what happens to the stored energy?

Accepted Answer

It increases by a factor of $$K.$$

Question 14

Which of the following is a correct statement about the effect of a dielectric on a capacitor with fixed free charge?

Accepted Answer

The potential difference decreases by a factor of $$K.$$

Question 15

Which of the following best describes the difference between polar and nonpolar molecules in a dielectric under an applied electric field?

Accepted Answer

Polar molecules align with the field due to permanent dipole moments; nonpolar molecules develop induced dipoles.

Question 16

A network of capacitors is simplified to a single equivalent capacitance $$C_{eq}. $$Which of the following is true for capacitors in series?

Accepted Answer

The charge on each capacitor is the same.

Question 17

A parallel-plate capacitor is charged and then disconnected from the battery. If the plate separation is doubled, what happens to the potential difference across the plates?

Accepted Answer

It doubles.

Question 18

Which of the following is the correct unit for capacitance?

Accepted Answer

Farad (F)

Capacitance and Dielectrics: Physics with Calculus Study Notes

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